Process management method and apparatus

ABSTRACT

Provided is a method of managing a target process. The method performed by a process management apparatus includes: generating a reference pattern indicating a normal state based on reference observed data on a process factor measured while the target process is maintained in the normal state; obtaining observed data on the process factor measured for a specified observation period; calculating a dissimilarity between the reference pattern and the observed data; and constructing a regression tree for the target process by using the observed data and the dissimilarity, wherein the process factor is set as an independent variable of the regression tree, and the dissimilarity is set as a dependent variable of the regression tree.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a divisional application of U.S. application Ser.No. 16/029,309, filed Jul. 6, 2018, which claims priority from KoreanPatent Application No. 10-2017-0101082, filed on Aug. 9, 2017, in theKorean Intellectual Property Office, the disclosure of which is hereinincorporated by reference in its entirety.

BACKGROUND 1. Field

The present inventive concept relates to a process management method andapparatus, and more particularly, to a process management method andapparatus employed to observe various process factors that affect thequality of a target process, detect an abnormality in the target processusing observed values, and optimize the target process.

2. Description of the Related Art

In the semiconductor field, maintaining product quality and achievingyield goals are very important. Since the quality and yield ofsemiconductors are greatly affected by the state of process equipmentthat performs a wafer processing process, it is essential to diagnoseand detect an abnormality early in the process in order to improve theyield of high-quality products. Therefore, various methods of quicklydetecting an abnormality in a semiconductor process are being proposed.

As sensors for observing various process factors affecting productquality increase in the semiconductor field and related observationtechnologies are developed, the amount of observation data collected isincreasing exponentially. Accordingly, a main paradigm of analysis ofobserved data is evolving from the perspective of descriptive analyticsor predictive analytics that simply detects an abnormality in a processinto the perspective of prescriptive analytics that detects a processfactor which is the cause of a process abnormality, provides an analysisof an abnormal state, and, at the same time, provides a guide forprocess optimization.

As related technologies, methods such as model-based automated processcontrol (MAPC) technology and run-to-run (R2R) control technology havebeen proposed.

However, the MAPC technology cannot provide an administrator with anintuitive guide for process optimization because it infers therelationship between a plurality of process factors that affect qualityby mostly using a neural network model which is a black box-type model.

The R2R control technology is a technology that dynamically controls aprocess factor to follow a target value in each unit run. The R2Rtechnology is widely used in modern industrial environments whereenvironmental and mechanical characteristics of a process indicating anormal state change over time. However, since the R2R control technologyobtains a target value of a process factor using a simple relationalexpression, it is difficult to obtain an accurate target value, and thecomplex interaction between process factors cannot be considered.

Therefore, there is a need for a method of providing an administratorwith intuitive guide information for process management and accuratelyperforming process management in consideration of the complicatedinteraction between process factors and the influence of each processfactor.

SUMMARY

Aspects of the inventive concept provide a method of managing a targetprocess by identifying a process factor that has a major influence on anabnormal state of the target process based on observed data on aplurality of process factors.

Aspects of the inventive concept also provide a method of generating amanagement rule for a target process in consideration of the interactionbetween a plurality of process factors and an individual influence indexof each process factor and optimizing the target process based on themanagement rule and an apparatus for performing the method.

Aspects of the inventive concept also provide a method of providingguide information for process management, such as identificationinformation of a process factor that has a major influence on anabnormal state of a target process and ruleset information indicating anormal state and the abnormal state of the target process, and anapparatus for performing the method.

However, aspects of the inventive concept are not restricted to the oneset forth herein. The above and other aspects of the inventive conceptwill become more apparent to one of ordinary skill in the art to whichthe inventive concept pertains by referencing the detailed descriptionof the inventive concept given below.

According to an aspect of the inventive concept, there is provided amethod of managing a target process using a process managementapparatus, the method comprising:

generating a reference pattern indicating a normal state based onreference observed data on a process factor measured while the targetprocess is maintained in the normal state; obtaining observed data onthe process factor measured for a specified observation period;calculating a dissimilarity between the reference pattern and theobserved data; and constructing a regression tree for the target processby using the observed data and the dissimilarity, wherein the processfactor is set as an independent variable of the regression tree, and thedissimilarity is set as a dependent variable of the regression tree.

According to another aspect of the inventive concept, there is provideda process management apparatus comprising: memory storing a plurality ofinstructions; and processor executing the plurality of instructions,wherein the plurality of instructions comprises: instructions forgenerating a reference pattern indicating a normal state based onreference observed data on a process factor measured while the targetprocess is maintained in the normal state; instructions for obtainingobserved data on the process factor measured for a specified observationperiod; instructions for calculating a dissimilarity between thereference pattern and the observed data; and instructions forconstructing a regression tree for the target process by using theobserved data and the dissimilarity, wherein the process factor is setas an independent variable of the regression tree, and the dissimilarityis set as a dependent variable of the regression tree.

BRIEF DESCRIPTION OF THE DRAWINGS

These and/or other aspects will become apparent and more readilyappreciated from the following description of the embodiments, taken inconjunction with the accompanying drawings in which:

FIG. 1 illustrates the configuration of a process management systemaccording to an embodiment of the inventive concept;

FIG. 2 is a diagram for explaining a multivariate management techniquethat can be referred to in some embodiments of the inventive concept;

FIG. 3 is a diagram for explaining a T-squared (T²) statistic that canbe referred to in some embodiments of the inventive concept;

FIGS. 4 and 5 are diagrams for explaining a limit in a T² control chart;

FIG. 6 is a block diagram of a process management apparatus according toan embodiment of the inventive concept;

FIG. 7 illustrates the hardware configuration of a process managementapparatus according to an embodiment of the inventive concept;

FIG. 8 is a first flowchart illustrating a process management methodaccording to an embodiment of the inventive concept;

FIG. 9 illustrates an exemplary user interface that can be referred toin some embodiments of the inventive concept;

FIGS. 10 and 11 are diagrams for explaining a method of constructing aregression tree that can be referred to in some embodiments of theinventive concept;

FIGS. 12 through 16 are diagrams for explaining a method of providingguide information for a target process based on a regression tree; and

FIG. 17 is a second flowchart illustrating a process management methodaccording to an embodiment of the inventive concept.

DETAILED DESCRIPTION

Hereinafter, preferred embodiments of the present invention will bedescribed with reference to the attached drawings. Advantages andfeatures of the present invention and methods of accomplishing the samemay be understood more readily by reference to the following detaileddescription of preferred embodiments and the accompanying drawings. Thepresent invention may, however, be embodied in many different forms andshould not be construed as being limited to the embodiments set forthherein. Rather, these embodiments are provided so that this disclosurewill be thorough and complete and will fully convey the concept of theinvention to those skilled in the art, and the present invention willonly be defined by the appended claims. Like numbers refer to likeelements throughout.

Unless otherwise defined, all terms including technical and scientificterms used herein have the same meaning as commonly understood by one ofordinary skill in the art to which this invention belongs. Further, itwill be further understood that terms, such as those defined in commonlyused dictionaries, should be interpreted as having a meaning that isconsistent with their meaning in the context of the relevant art and thepresent disclosure, and will not be interpreted in an idealized oroverly formal sense unless expressly so defined herein. The terms usedherein are for the purpose of describing particular embodiments only andis not intended to be limiting. As used herein, the singular forms areintended to include the plural forms as well, unless the context clearlyindicates otherwise.

It will be understood that the terms “comprise” and/or “comprising” whenused herein, specify some stated components, steps, operations and/orelements, but do not preclude the presence or addition of one or moreother components, steps, operations and/or elements.

Prior to description of this specification, some terms to be used hereinwill be clarified.

In the present specification, process management can be understood as acomprehensive concept including observing process factors that mayaffect the quality of a target process in order to achieve apredetermined purpose, detecting an abnormality in the target processbased on observed values, and controlling the target process to beoptimized.

In the present specification, process factors can be understood as acomprehensive concept including all elements that can be observed bysensors. For example, in the field of semiconductors, the processfactors may be set to factors that may affect the quality of asemiconductor, such as temperature, pressure, and humidity. Depending onthe technical field, the process factors can be used interchangeablywith terms such as process parameters, variables, observation factors,and parameters to refer to the same things.

Embodiments of the inventive concept will hereinafter be described indetail with reference to the accompanying drawings.

FIG. 1 illustrates the configuration of a process management systemaccording to an embodiment of the inventive concept.

Referring to FIG. 1, the process management system is a system thatobserves a plurality of process factors such as temperature, humidityand pressure using sensors 20 a through 20 n, detects an abnormality ina target process (e.g., process equipment 10) based on observed datacollected by the sensors 20 a through 20 n, and controls the targetprocess to be performed in an optimized state. For example, the processmanagement system may be an automatic process control (APC) system thatcontrols a target process in real time in the semiconductor field.

In the current embodiment the process management system may beconfigured to include the sensors 20 a through 20 n and a processmanagement apparatus 100. However, this is merely an embodiment forachieving the objectives of the inventive concept, and some componentscan be added or deleted as needed. In addition, it should be noted thatthe components of the process management system illustrated in FIG. 1are functionally distinct components and that one or more components canbe integrated with each other in an actual physical environment. Eachcomponent of the process management system will now be described.

In the process management system, the sensors 20 a through 20 n aredevices for observing a plurality of process factors that may affect atarget process. The sensors 20 a through 20 n may provide observed dataon the process factors to the process management apparatus 100.

In the process management system, the process management apparatus 100is a computing device that can monitor and control a target processoverall. Here, the computing device may be implemented as a device suchas a notebook computer, a desktop computer, or a laptop computer.However, the computing device is not limited to these examples and canbe implemented as any device including a computing unit and acommunication unit.

According to an embodiment of the inventive concept, the processmanagement apparatus 100 may perform process management using amultivariate management technique in order to consider the correlationbetween process factors. The current embodiment will be furtherdescribed with reference to FIG. 2.

FIG. 2 is a diagram for comparing a case where process management isperformed using a univariate control chart for each of two processfactors X1 and X2 and a case where process management is performed usinga multivariate control chart according to the current embodiment. InFIG. 2, “LCL” and “UCL” represent a lower control limit and an uppercontrol limit, respectively. In particular, a T-squared (T²) controlchart is illustrated as an example from among multivariate controlcharts.

Referring to FIG. 2, observed data 31 a and 31 b are all in a normalrange in the univariate control chart. Therefore, an abnormal signal isnot venerated. In the T² control chart, however, since the correlationbetween process factors included in observed data 31 is taken intoconsideration, the observed data 31 is sensed to correspond to anoutlier outside the normal range. Therefore, the process managementapparatus 100 using a multivariate management technique can easilydetect a process abnormality that is difficult to detect using aunivariate management technique.

In order to facilitate understanding, the T² control chart will bebriefly described. The T² control chart refers to a multivariatemanagement technique that manages a process based on Hotelling's T²statistic. Here, the T² statistic is one statistic into which measuredvalues of a plurality of process factors are summarized. The T²statistic can be understood as a value indicating how far an observedvalue is from a mean vector indicating a reference distribution e.g., adistribution of normal data). More specifically, the T² statistic refersto a Mahalanobis distance between a mean vector and an observed value.The Mahalanobis distance is different from a Euclidean distance in thatit is a value calculated by further taking into consideration thevariance of the reference distribution. Therefore, referring to FIG. 3,an observed value B, which is at a closer distance based on theEuclidean distance, may be at a greater distance based on theMahalanobis distance.

In the multivariate management technique, the correlation or interactionbetween process factors can be considered overall, but analysis logic isrequired to identify an individual influence index of each processfactor. Here, the individual influence index can be understood as thedegree of influence of a process factor on a target process.

For example, referring to observed data on process factors X1 and X2illustrated in FIG. 4 and a T² control chart illustrated in FIG. 5,drift patterns 41 and 43 are observed from about 500^(th) observedvalues of the process factors X1 and X2, and thus an abnormal phenomenonof exceeding a control limit 45 is detected in the T² control chart.However, since the T² statistic provides only one summarized statisticalinformation, the individual influence index of each of the processfactors X1 and X2 cannot be identified in the T² control chart.Furthermore, if the respective observed values of the process factors X1and X2 are similar as illustrated in FIG. 4, an administrator of atarget process cannot effectively manage the target process because heor she cannot identify a process factor that has a major influence onthe target process from among the process factors X1 and X2. Therefore,analysis logic is needed to identify a process factor that has a majorinfluence on an abnormal state of the target process and to provideguide information for process management to the administrator.

For reference, the control limit 45 illustrated in FIG. 5 can be set invarious ways. For example, assuming that observed data follows amultivariate normal distribution, the T² statistic will folioF-distribution. Therefore, the control limit may be set based on theF-distribution. A method of setting a control limit based on theF-distribution is obvious to those of ordinary skill in the art, andthus a description of the method will be omitted. The description willbe continued with reference to FIG. 1 again.

According to an embodiment of the inventive concept, the processmanagement apparatus 100 may identify a process factor that has a majorinfluence on a process abnormality using a regression tree constructedbased on observed data and may provide intuitive guide informationprocess management to an administrator. Here, the guide information mayinclude an individual influence index of each process factor, a normalruleset indicating a normal state, an abnormal ruleset indicating anabnormal state, and the like. In addition, since the regression tree, byits nature, can be intuitively analyzed, it may be included in the guideinformation. A detailed description of the current embodiment will begiven later with reference to FIGS. 8 through 16.

According to an embodiment of the inventive concept, the processmanagement apparatus 100 may alert the administrator when detecting anabnormality using a ruleset which is structured guide information andmay automatically control a target process to be optimized. This will bedescribed in detail later with reference to FIG. 17.

In the process management system illustrated in FIG. 1, the processmanagement apparatus 100 may receive observed data from various sensors20 a through 20 n through a network. Here, the network may beimplemented as any kind of wired/wireless network such as a local areanetwork (LAN), a wide area network (WAN), a mobile radio communicationnetwork, or a wireless broadband Internet (Wibro).

Until now, the process management system according to the embodiment ofthe inventive concept has been described with reference to FIGS. 1through 5. The configuration and operation of a process managementapparatus 100 according to an embodiment of the inventive concept willnow be described with reference to FIGS. 6 and 7.

FIG. 6 is a block diagram of a process management apparatus 100according to an embodiment of the inventive concept.

Referring to FIG. 6, the process management apparatus 100 may beconfigured to include a reference pattern generation unit 110, adissimilarity calculation unit 120, a regression tree construction unit130, and a ruleset generation unit 140. In FIG. 6, components onlyrelated to the embodiment of the inventive concept are illustrated.Therefore, it will be understood by those of ordinary skill in the artto which the inventive concept pertains that other general-purposecomponents can be included in addition to the components illustrated inFIG. 6. In addition, it should be noted that the components of theprocess management apparatus 100 illustrated in FIG. 6 are functionallydistinct components and that one or more components can be integratedwith each other in an actual physical environment.

Referring to each component, the reference pattern generation unit 110generates a reference pattern based on which dissimilarity iscalculated. For example, the reference pattern generation unit 110 maygenerate a reference pattern indicating a normal state by usingreference observed data observed while a target process is maintained inthe normal state. Alternatively, the reference pattern generation unit110 may generate the reference pattern using reference observed data onan abnormal state. Unless otherwise stated, the reference pattern willbe assumed as a pattern indicating the normal state. A method by whichthe reference pattern generation unit 110 generates the referencepattern will be described in detail later with reference to FIG. 8.

The dissimilarity calculation unit 120 calculates the dissimilaritybetween the reference pattern and observed data. A method of calculatingthe dissimilarity will be described in detail later with reference toFIG. 8.

The regression tree construction unit 130 constructs a regression treeusing observed data and dissimilarity. According to an embodiment of theinventive concept, the regression tree construction unit 130 mayconstruct the regression tree by setting process factors of the observeddata as independent variables and setting the dissimilarity as adependent variable. The construction of the regression tree will bedescribed in detail later with reference to FIGS. 8, 10 and 11.

The ruleset generation unit 140 generates various kinds of rulesetsusing a regression tree. For example, the ruleset generation unit 140may generate a normal ruleset 150 indicating the normal state of atarget process and an abnormal ruleset 160 indicating the abnormal stateof the target process. A method by which the ruleset generation unit 140generates a ruleset from a regression tree will be described in detaillater with reference to FIGS. 8 and 13 through 16.

According to an embodiment of the inventive concept, the processmanagement apparatus 100 may further include a user interface unit (notillustrated). The user interface unit (not illustrated) may receivevarious information necessary for process management from anadministrator through a graphic user interface (GUI). Alternatively, theadministrator may provide various guide information necessary forprocess management. An example of the GUI is illustrated in FIGS. 9 and11.

According to an embodiment of the inventive concept, the processmanagement apparatus 100 may further include a control unit (notillustrated). The control unit (not illustrated) may detect anabnormality in a target process in real time using the normal ruleset150 and/or the abnormal ruleset 160 or may control process factors sothat the target process is maintained in an optimized state. Forexample, when detecting observed data that exceeds a control limit, thecontrol unit (not illustrated) may determine a target process to be inthe abnormal state and alert the administrator. Alternatively, whenobserved data satisfies the abnormal ruleset 160, the control unit (notillustrated) may determine the target process to be in the abnormalstate and alert the administrator. The control unit (not illustrated)will be further described later with reference to FIG. 17.

Each component of the process management apparatus 100 illustrated inFIG. 6 may be, but is not limited to, a software component or a hardwarecomponent such as a Field Programmable Gate Array (FPGA) or ApplicationSpecific Integrated Circuit (ASIC). A component may advantageously beconfigured to reside on the addressable storage medium and configured toexecute on one or more processors. The functionality provided for in thecomponents may be further separated into additional components orcombined into a single component that performs certain functions.

FIG. 7 illustrates the hardware configuration of a process managementapparatus 100 according to an embodiment of the inventive concept.

Referring to FIG. 7, the process management apparatus 100 may includeone or more processors 101, a bus 105, a network interface 107, a memory103 which loads a computer program to be executed by the processors 101,and a storage 109 which stores process management software 109 a. InFIG. 7, components only related to the embodiment of the inventiveconcept are illustrated. Therefore, it will be understood by those ofordinary skill in the art to which the inventive concept pertains thatother general-purpose components can be included in addition to thecomponents illustrated in FIG. 7.

The processors 101 control the overall operation of each component ofthe process management apparatus 100. The processors 101 may include acentral processing unit (CPU), a micro-processor unit (MPU), amicro-controller unit (MCU), a graphic processing unit (GPU), or anyform of processor well known in the art to which the inventive conceptpertains. In addition, the processors 101 may perform an operation on atleast one application or program for executing a method according toembodiments of the inventive concept. The process management apparatus100 may include one or more processors.

The memory 103 stores various data, commands and/or information. Thememory 103 may load one or more programs 109 a from the storage 109 toexecute a process management method according to embodiments. In FIG. 7,a random access memory (RAM) is illustrated as an example of the memory103.

The bus 105 provides a communication function between the components ofthe process management apparatus 100. The bus 105 may be implemented asvarious forms of buses such as an address bus, a data bus and a controlbus.

The network interface 107 supports wired and wireless Internetcommunication of the process management apparatus 100. In addition, thenetwork interface 107 may support various communication methods as wellas Internet communication. To this end, the network interface 107 mayinclude a communication module well known in the art to which theinventive concept pertains.

The storage 109 may non-temporarily store reference observed dataobserved when a target process is in a normal state, observed data onprocess factors measured during a specified observation period, and theprograms 109 a. In FIG. 7, the process management software 109 a isillustrated as an example of the programs 109 a.

The storage 109 may include a non-volatile memory such as a read onlymemory (ROM), an erasable programmable ROM (EPROM), an electricallyerasable programmable ROM (EEPROM) or a flash memory, a hard disk, aremovable disk, or any form of computer-readable recording medium wellknown in the art to which the inventive concept pertains.

The process management software 109 a may perform a process managementmethod according to an embodiment of the inventive concept.Specifically, the process management software 109 a may be loaded intothe memory 103 and executed by the processors 101 to perform anoperation of generating a reference pattern indicating the normal statebased on the reference observed data, an operation of calculating thedissimilarity between the reference pattern and the observed data, andan operation of constructing a regression tree for the target process byusing the observed data and the dissimilarity.

Until now, the configuration and operation of the process managementapparatus 100 according to the embodiment of the inventive concept havebeen described with reference to FIGS. 6 and 7. A process managementmethod according to an embodiment of the inventive concept will now bedescribed in detail with reference to FIGS. 8 through 16.

Each operation included in the process management method according tothe embodiment of the inventive concept may be performed by a computingdevice. The computing device may be, for example, the process managementapparatus 100. However, the subject of each operation included in theprocess management method may be omitted for ease of description. Inaddition, each operation included in the process management method maybe an operation performed by the process management apparatus 100 as theprocess management software 109 a is executed by the processors 101.

FIG. 8 is a flowchart illustrating a process management method accordingto an embodiment of the inventive concept. However, this is merely anembodiment for achieving the objectives of the inventive concept, andsome operations can be added or removed if necessary.

Referring to FIG. 8, the process management apparatus 100 generates areference pattern indicating a normal state based on reference observeddata on process factors measured while a target process is maintained inthe normal state (operation S100). Here, the reference pattern may be acharacteristic value representing the reference observed data and can beobtained in any way which may vary depending on a dissimilaritycalculation method.

For example, when dissimilarity is calculated based on the T² statistic,the reference pattern may be calculated as a mean vector of thereference observed data. In another example, when the dissimilarity iscalculated based on the Euclidean distance, the reference pattern may becalculated as an average point of the reference observed data or acentroid of a cluster of the reference observed data. In anotherexample, when the dissimilarity is calculated based on a model residual,the reference pattern may be a machine learning model, a statisticalmodel, or the like constructed based on the reference observed data.

According to an embodiment of the inventive concept, the referenceobserved data may be updated to latest data at a specified time or inpredetermined cycles. In addition, the reference pattern may begenerated again using the updated reference observed data. This isintended to reflect the fact that internal and external factors thataffect the quality of the target process can change over time. Forexample, in a semiconductor process, a temperature range, a pressurerange, etc. indicating that a process is in the normal state can varyaccording to changes in the external environment. According to thecurrent embodiment, since the reference pattern can be adaptivelyupdated according to the internal and external factors that can changedynamically, process management can be effectively performed even in adynamic environment such as a modern industrial environment.

Next, the process management apparatus 100 obtains observed data on theprocess factors measured for a specified observation period (operationS200). For example, the process management apparatus 100 may receive theobserved data from various sensors that measure the process factors ofthe target process.

In an embodiment, the specified observation period may be determinedautomatically by the process management apparatus 100. For example, theprocess management apparatus 100 may determine a period in which eachunit process is performed as the observation period. In another example,when detecting an abnormal state of the target process, the processmanagement apparatus 100 may determine a period including first observeddata indicating the normal state and second observed data indicating theabnormal state as the observation period. In another example, whendetecting the abnormal state of the target process, the processmanagement apparatus 100 may determine a period including only observeddata indicating the abnormal state as the observation period.

In the above-described embodiment, a case where the abnormal state isdetected may be a case where dissimilarity to be described later exceedsa preset control limit or a case where observed data satisfies at leastone rule included in an abnormal ruleset.

In an embodiment, the specified observation period may be set through auser interface provided by the process management apparatus 100. Forexample, the process management apparatus 100 may provide an exemplaryuser interface illustrated in FIG. 9 to an administrator. Through theexemplary user interface, the administrator may receive observationinformation such as the T² statistic and observed data on a plurality ofprocess factors (X1 and X2). In this case, the administrator maydesignate a period including observed data to be analyzed as theobservation period by, e.g., a dragging method as illustrated in FIG. 9.In FIG. 9, a period in which the state changes from the normal state tothe abnormal state is set as the observation period in order to analyzethe cause of the abnormal state.

Referring again to FIG. 8, the process management apparatus 100calculates the dissimilarity between the observed data and the referencepattern (operation S300).

In an embodiment, the dissimilarity may be calculated based on the T²statistic, which is a multivariate management technique, in order toconsider the correlation between a plurality of process factors.

In an embodiment, the dissimilarity may be calculated based on theEuclidean distance in order for simple implementation.

The dissimilarity may also be calculated based on a novelty score, amodel residual, or the like. The dissimilarity can be calculated in anyway as long as it can represent the difference between the observed dataand the reference pattern.

Next, the process management apparatus 100 constructs a regression treefor the target process by using the observed data and the dissimilarity(operation S400). Specifically, the process management apparatus 100constructs a regression tree by setting each process factor as anindependent variable and setting the dissimilarity as a dependentvariable as illustrated in FIG. 10. Since the process managementapparatus 100 does not construct a classification tree, which is anexample of a decision tree, it constructs a regression tree by settingthe dissimilarity as a dependent variable instead of setting the normalstate and the abnormal state as dependent variables.

The process management apparatus 100 constructs a regression tree insuch a manner that the variance of a dependent variable corresponding toeach tree node is minimized. That is, the process management apparatus100 constructs the regression tree in such a manner that informationentropy of the observed data is minimized and the information gain ofthe observed data is maximized. Since this is a concept widely known inthe art, a description thereof will be omitted. The process managementapparatus 100 may also construct a regression tree using a regressiontree construction algorithm (e.g., CART, GUIDE, M5, etc.) widely knownin the art.

The variance of the dependent variable indicating the informationentropy may be calculated according to Equation 1 below, and theinformation gain may be calculated according to Equation 2 below. InEquation 1, xc indicates an average value of a dependent variablecorresponding to each tree node c, and yi indicates a dependent variablevalue for an i^(th) piece of observed data from among observed datacorresponding to each tree node.

$\begin{matrix}{{{SS} = {\sum\limits_{c \in \;{nodes}}{\sum\limits_{i \in c}\left( {y_{i} - {\overset{\_}{x}}_{c}} \right)^{2}}}}{where}{{{\overset{\_}{x}}_{c} = {\frac{1}{n_{c}}{\sum_{i \in c}y_{i}}}},}} & {(1).}\end{matrix}$

In addition, in Equation 2, j indicates a variable used for division, pindicates a division point, R0 indicates data before a tree node isdivided, and R1 and R2 indicate data after the tree node is divided.

$\begin{matrix}{{\underset{j,p}{argmin}\mspace{11mu}\left\lbrack {{\sum\limits_{x_{i} \in {R_{1}{({j,p})}}}{ss}_{i}} + {\sum\limits_{x_{i} \in {R_{2}{({j,p})}}}{ss}_{i}} - {\sum\limits_{x_{i} \in R_{0}}{ss}_{i}}} \right\rbrack}{where}{{{R_{1}\left( {j,p} \right)} = \left\{ {X❘{{X_{j} \leq {p\mspace{14mu}{and}\mspace{14mu} X}} \in R_{0}}} \right\}},{{R_{2}\left( {j,p} \right)} = \left\{ {X❘{{X_{j} > {p\mspace{14mu}{and}\mspace{14mu} X}} \in R_{0}}} \right\}}}} & (2)\end{matrix}$

According to an embodiment, the process management apparatus 100 mayperform a pruning process through cross validation in order to preventover-fitting of the regression tree.

The regression tree constructed in operation S400 will be describedlater with reference to FIG. 11.

Referring again to FIG. 8, the process management apparatus 100generates a ruleset for managing the target process by using theregression tree constructed in operation S400 (operation S500). Theruleset may include a normal ruleset indicating the normal state of thetarget process and an abnormal ruleset indicating the abnormal state ofthe target process. In addition, the ruleset is one of the guideinformation provided to the administrator. The ruleset can be utilizedby the administrator for process management and can be utilized asreference information for automatically controlling each process factor.Operation S500 will be described in detail later with reference to FIGS.12 through 17.

Until now, the process management method according to the embodiment ofthe inventive concept has been described with reference to FIGS. 8through 10. According to the above-described method, a regression treeis constructed by setting a plurality of process factors as independentvariables and setting the dissimilarity between a reference pattern andobserved data as a dependent variable. Therefore, it is possible togenerate a reliable ruleset that reflects the interaction between theprocess factors and an individual influence index of each processfactor.

A regression tree that can be referred to in some embodiments of theinventive concept will now be described with reference to FIG. 11.

FIG. 11 illustrates an exemplary regression tree that can be constructedin operation S400. Specifically, FIG. 11 illustrates an exemplaryregression tree constructed by setting process factors such as pressure,temperature and current as independent variables and settingdissimilarity based on the T² statistic as a dependent variable. Theregression tree may be guide information provided to the administratorthrough a user interface.

Referring to FIG. 11, the regression tree may be composed of, e.g., aplurality of layers and a plurality of tree nodes, and the tree nodesmay be divided based on a specific value of a process factor due to thenature of the regression tree. For example, it can be seen that a treenode 53 and a tree node 55 are divided based on a specific value (1.076)of a process factor (pressure).

Each tree node included in the regression tree may correspond toobserved data that satisfies a specific condition for a process factor.For example, it can be seen that the tree node 53 corresponds toobserved data with a pressure of “less than 1.076” and that the numberof pieces of observed data corresponding to the tree node 53 is “109.”In addition, it can be seen that an average dissimilarity value of theobserved data corresponding to the tree node 53 is “7.3813.” Since theregression tree can be understood clearly by those of ordinary skill inthe art, a further description of the regression tree will be omitted.

A method of providing guide information for a target process based on aregression tree will now be described with reference to FIGS. 12 through16.

According to an embodiment of the inventive concept, the processmanagement apparatus 100 may provide, as guide information, informationabout a process factor that has a major influence on the abnormal stateof a target process and about an individual influence index of eachprocess factor. This will now be described with reference to FIG. 12.

FIG. 12 illustrates an example of a regression tree that can beconstructed in operation S400. Specifically, FIG. 12 illustrates aregression tree constructed by setting a first process factor X1 and asecond process factor X2 as independent variables and using firstobserved data on the normal state and second observed data on theabnormal state.

When the regression tree is constructed as illustrated in FIG. 12, anindividual influence index of each process factor X1 or X2 may bedetermined based on the order in which the process factors X1 and X2 areused to divide tree nodes of the regression tree. Specifically, it maybe determined that the first process factor X1 used to divide tree nodes61 and 63 located in a first layer has a higher individual influenceindex than the second process factor X2 used to divide tree nodes 65 and67 located in a second laver. This is because, when a regression tree isconstructed such that the variance value of dissimilarity, which is adependent variable, is minimized, tree nodes are preferentially dividedby a process factor that has the greatest influence on thedissimilarity.

Therefore, if the regression tree is constructed as illustrated in FIG.12, the process management apparatus 100 may, when detecting a processabnormality, provide the administrator with guide information indicatingthat the first process factor X1 should be controlled prior to thesecond process factor X2. For reference, when tree nodes in the samelayer are divided by different process factors, individual influenceindices of the different process factors may be determined by comparinginformation values obtained from the division.

In addition, according to an embodiment of the inventive concept, theprocess management apparatus 100 may give a higher control priority tothe first process factor X1 than to the second process factor X2 and,when detecting a process abnormality, may operate to preferentiallycontrol the first process factor X1.

Next, a method of generating a ruleset, which is structured guideinformation, based on a regression tree in operation S500 will bedescribed with reference to FIGS. 13 through 16.

According to an embodiment of the inventive concept, the processmanagement apparatus 100 does not generate a ruleset based on onlyterminal nodes of a regression tree, but generates a ruleset based ontree nodes selected according to various criteria. Therefore, a rulesetcan be generated based on tree nodes located in a middle layer of theregression tree. Some embodiments in which the process managementapparatus 100 generates a ruleset will now be described.

In an embodiment, the process management apparatus 100 may generate anormal ruleset indicating the normal state and an abnormal rulesetindicating the abnormal state based on an average dissimilarity value(e.g., a T² statistic) corresponding to each tree node included in aregression tree. For example, referring to FIG. 13, the processmanagement apparatus 100 may generate a normal ruleset based on treenodes 71 whose average dissimilarity values are equal to or less than apreset first threshold value and generate an abnormal ruleset based ontree nodes 73 whose average dissimilarity values are equal to or greaterthan a preset second threshold value. Here, the first threshold valueand the second threshold value may be values determined based on, forexample, a control limit. In FIG. 13, the first threshold value is “9,”and the second threshold value is “11.”

In addition, the process management apparatus 100 may provide, as anoptimal rule, a rule generated based on a tree node having a smallestaverage dissimilarity value from among rules included in the normalruleset. For example, an optimal rule may be generated based on a treenode 71 a illustrated in FIG. 13 and may be generated as “if pressure<1.076 & current 5.253, then normal (optimal).” The optimal rule may beprovided to the administrator as guide information and may be utilizedas reference information for controlling a target process. For example,the process management apparatus 100 may control observed values ofprocess factors to be included in the range of the optimum rule in asubsequent process.

In an embodiment, the process management apparatus 100 may select treenodes whose corresponding average dissimilarity values exceed a presetcontrol limit from among tree nodes included in a regression tree andgenerate an abnormal ruleset indicating the abnormal state of a targetprocess using the selected tree nodes. In addition, the processmanagement apparatus 100 may monitor the target process based on theabnormal ruleset and alert the administrator.

In an embodiment, the process management apparatus 100 may select treenodes based on the average and degree of deviation (e.g., variance orstandard deviation) of dissimilarity values corresponding to each treenode of a regression tree and generate a normal ruleset and/or anabnormal ruleset based on the selected tree nodes. For example, theprocess management apparatus 100 may select tree nodes whose weightedsums of the average and variance of dissimilarity values are equal to orless than a threshold value and generate a normal ruleset using. theselected tree nodes. In another example, the process managementapparatus 100 may select candidate nodes from among the tree nodesincluded in the regression tree based on the average of dissimilarityvalues and generate a normal ruleset or an abnormal ruleset based ontree nodes whose variances of dissimilarity values are equal to or lessthan a threshold value from among the candidate nodes. According to thecurrent embodiment, since the degree of deviation of dissimilarityvalues is further considered, a more reliable ruleset can be generated.

In an embodiment, the process management apparatus 100 may select treenodes by further considering the number of pieces of observed datacorresponding to each tree node and generate a normal ruleset or anabnormal ruleset based on the selected tree nodes. For example, theprocess management apparatus 100 may generate a normal ruleset based ontree nodes whose corresponding averages and degrees of deviation ofdissimilarity values are equal to or less than threshold values andwhose numbers of pieces of observed data are equal to or greater than athreshold value. This is because the smaller the average and degree ofdeviation of dissimilarity values and the greater the number of piecesof observed data, the better the observed data represents a normalpattern. In another example, the process management apparatus 100 mayselect tree nodes based on the weighted sum of the average and degree ofdeviation of dissimilarity values and the number of pieces of observeddata and generate a normal ruleset and an abnormal ruleset based on theselected tree nodes. FIGS. 14 and 15 illustrate an example of generatingan optimal ruleset according to the current embodiment.

Specifically, FIG. 14 illustrates a regression tree constructed in acase where a third process factor X3 has a highest individual influenceindex from among three process factors X1, X2 and X3 set as independentvariables. The values shown in a tree node of the regression treeillustrated in FIG. 14 are an average dissimilarity value (2.63) basedon the T² statistic, the number of pieces of observed data (559) and aratio (55.9%), respectively. Intermediate nodes are not illustrated forease of description.

Referring to FIG. 14, when tree nodes are selected in consideration ofthe average and degree of deviation of dissimilarity values and thenumber of pieces of observed data corresponding to each tree nodeincluded in the regression tree, a tree node 83, which is not a terminalnode, is selected as a node for generating an optimal ruleset. Anoptimal ruleset 87 generated based on the tree node 83 is shown in FIG.15.

In addition, FIGS. 14 and 16 illustrate an example of generating anabnormal ruleset based on tree nodes 85 whose averages of dissimilarityvalues exceed a preset control limit or a predetermined threshold value.An example of the generated abnormal ruleset is shown in FIG. 16.

In the embodiments described so far, it is assumed that all the treenodes included in a regression tree are searched in order to select atree node serving as a basis for generating an optimal ruleset. However,according to an embodiment of the inventive concept, the search may beperformed in a direction from an upper layer toward a lower layer of theregression tree so that a value calculated according to Equation 3 belowis minimized.

In Equation 3, c-1 indicates a node (e.g., a parent node) of an upperlayer, and c indicates a node (e.g., a child node) of a lower layer. Inaddition, xc indicates an average dissimilarity value of a tree node C,ssc indicates the variance of dissimilarity values, nc indicates thenumber of pieces of observed data (coverage), and W indicates a weightvalue. The weight value may be an experimentally determined value.However, if the reliability of a rule is important, a relatively highweight value may be given to the variance.

$\begin{matrix}{{{argmin}_{c}\left\lbrack {{{Wx}\frac{{\overset{\_}{x}}_{c}}{{\overset{\_}{x}}_{c} - 1}} + {{Wss}\frac{{ss}_{c}}{{ss}_{c - 1}}} + {{Wn}\left( {1 - \frac{n_{c}}{n_{c - 1}}} \right)}} \right\rbrack}{where}{{\sum W} = 1.}} & (3)\end{matrix}$

Referring to Equation 3, it can be understood that a search is performedin a direction from the upper node c-1 to the lower node c which has asmaller average and variance of dissimilarity values than the upper nodec and whose number of pieces of observed data is slightly different fromthat of the upper node c from among a plurality of lower nodes.

For specific example, in the regression tree illustrated in FIG. 11 andFIG. 13, a search direction may be determined to be a direction from aroot node to a node having a smaller value calculated according toEquation 3 between a left child node and a right child, node of the rootnode. Here, the process management apparatus 100 proceeds to search theleft child node with a smaller average dissimilarity value and a largernumber of pieces of observed data.

Until now, the method of providing guide information for a targetprocess based on a regression tree has been described with reference toFIGS. 12 through 16, According to the above-described method, theindividual influence index of each process factor can be calculatedbased on the order in which the process factors are used to divide treenodes of the regression tree. Therefore, it is possible to provideidentification information of a process factor that has a majorinfluence on the abnormal state of the target process. This makeseffective process management possible. In addition, intuitive guideinformation such as major process factors, a normal ruleset and anabnormal ruleset can be provided to the administrator based on theregression tree. Therefore, the convenience of the administratorperforming process management can be increased. Furthermore, the guideinformation is used as recipe optimization logic of process equipment,thereby contributing to improvement of product quality and yield.

A process management method according to an embodiment of the inventiveconcept will now be described with reference to FIG. 17.

According to the embodiment of the inventive concept, the processmanagement apparatus 100 may automatically control a target processusing a ruleset venerated as described above. More specifically, whenthe same unit process is repeated, the process management apparatus 100may construct a regression tree based on observed data of a first unitprocess, generate a ruleset for managing a unit process based on theregression tree, and automatically manage a second unit process, whichis a unit process subsequent to the first unit process, using theruleset.

Referring to the flowchart illustrated in FIG. 17, the processmanagement apparatus 100 receives, in real time, observed data onprocess factors measured while a first unit process is performed andconstructs a regression tree for the first unit process based on theobserved data (operations S600, S700 and S800). A description ofoperations S600, S700 and S800 is omitted in order to avoid redundancy.

Next, the process management apparatus 100 generates a ruleset forcontrolling a second unit process performed after the first unit processby using the regression tree (operation S900). For example, according tothe above-described embodiments, the process management apparatus 100may generate a normal ruleset including an optimal ruleset and anabnormal ruleset indicating an abnormal state.

Next, the process management apparatus 100 manages the second unitprocess using the generated ruleset (operation S1000). For example, theprocess management apparatus 100 may control process factors of thesecond unit process according to the range of process factors includedin the optimal ruleset. In another example, the process managementapparatus 100 may detect the abnormal state of the second unit processusing the abnormal ruleset and alert the administrator.

Until now, the process management method according to the embodiment ofthe inventive concept has been described with reference to FIG. 17.According to the above-described method, a normal ruleset indicating thenormal state of a target process can be generated based on a regressiontree, and optimization of the target process can be automaticallyperformed using the normal ruleset. Accordingly, this can increase theconvenience of process management and improve the quality and yield ofproducts, particularly in the field of production process. In addition,an abnormal ruleset indicating the abnormal state of the target processcan be generated based on the regression tree, anti an abnormality inthe target process can be accurately detected using the abnormalruleset.

The concepts of the invention described above with reference to FIGS. 1to 17 can be embodied as computer-readable code on a computer-readablemedium. The computer-readable medium may be, for example, a removablerecording medium (a CD, a DVD, a Blu-ray disc, a USB storage device, ora removable hard disc) or a fixed recording medium (a ROM, a RAM, or acomputer-embedded hard disc). The computer program recorded on thecomputer-readable recording medium may be transmitted to anothercomputing apparatus via a network such as the Internet and installed inthe computing apparatus. Hence, the computer program can be used in thecomputing apparatus.

Although operations are shown in a specific order in the drawings, itshould not be understood that desired results can be obtained when theoperations must be performed in the specific order or sequential orderor when all of the operations must be performed. In certain situations,multitasking and parallel processing may be advantageous. According tothe above:-described embodiments, it should not be understood that theseparation of various configurations is necessarily required, and itshould be understood that the described program components and systemsmay generally be integrated together into a single software product orbe packaged into multiple software products.

While the present invention has been particularly illustrated anddescribed with reference to exemplary embodiments thereof, it will beunderstood by those of ordinary skill in the art that various changes inform and detail may be made therein without departing from the spiritand scope of the present invention as defined by the following claims.The exemplary embodiments should be considered in a descriptive senseonly and not for purposes of limitation.

What is claimed is:
 1. A method of managing a target process using aprocess management apparatus comprising at least one processor, themethod comprising: generating a reference pattern that indicates anormal state based on reference data about a first process factor amonga plurality of process factors associated with the target process, thefirst process factor measured while the target process is maintained inthe normal state; obtaining observed data, collected by at least onesensor, on the first process factor measured for an observation period;calculating a dissimilarity between the reference pattern and theobserved data; constructing a regression tree for the target process byusing the observed data and the dissimilarity; and controlling a secondprocess factor among the plurality of process factors based on theregression tree, wherein the first process factor is set as anindependent variable of the regression tree, and the dissimilarity isset as a dependent variable of the regression tree.
 2. The method ofclaim 1, wherein the generating of the reference pattern comprises:updating the reference data to data that is more recent than thereference data; and generating the reference pattern again by using theupdated reference data.
 3. The method of claim 1, wherein the processfactor is provided in plural numbers, and the dissimilarity iscalculated based on Hotelling's T-squared (T2) statistic.
 4. The methodof claim 1, wherein the observed data comprises first observed dataobserved when the target process is in the normal state and secondobserved data observed when the target process is in an abnormal state.5. The method of claim 1, wherein the constructing of the regressiontree comprises selecting abnormal observed data, the abnormal observeddata comprising dissimilarity values exceeding a preset control limit,from the observed data and constructing the regression tree for thetarget process by using the abnormal observed data and the dissimilarityvalues of the abnormal observed data, and generating a rulesetindicating an abnormal state of the target process by using theregression tree.
 6. The method of claim 1, wherein the controlling thesecond process factor based on the regression tree comprises: generatinga ruleset based on one or more tree nodes selected from tree nodesincluded in the regression tree; and controlling the second processfactor based on the generated ruleset, wherein the selected tree nodesare not terminal nodes.
 7. The method of claim 1, wherein thecontrolling the second process factor based on the regression treecomprises: selecting a tree node with a corresponding averagedissimilarity value that is smallest among the tree nodes included inthe regression tree; generating a ruleset indicating an optimal state ofthe target process based on the selected tree node; and controlling thesecond process factor based on the generated ruleset.
 8. The method ofclaim 1, wherein the controlling the second process factor based on theregression tree comprises: selecting one or more tree nodes from thetree nodes included in the regression tree based on an average anddegree of deviation of dissimilarity values corresponding to each treenode; generating a ruleset indicating the normal state of the targetprocess based on the selected one or more tree nodes; and controllingthe second process factor based on the generated ruleset.
 9. The methodof claim 8, wherein the selecting of the one or more tree nodes from thetree nodes included in the regression tree comprises selecting the treenodes based on a number of pieces of observed data corresponding to eachtree node.
 10. The method of claim 8, wherein the target processincludes a first unit process and a second unit process, wherein theobserved data is observed data on the first unit process, and whereinthe generated ruleset includes a first range of process factor valuesindicating the normal state, wherein the controlling the second processfactor based on the generated ruleset comprises, controlling the secondprocess factor value to be included in the first range of process factorvalues while the second unit process is performed.
 11. The method ofclaim 1, wherein the controlling the second process factor based on theregression tree comprises: selecting first tree nodes with correspondingaverage dissimilarity values equal to or less than a first thresholdvalue from the tree nodes included in the regression tree, andgenerating a first ruleset indicating the normal state of the targetprocess based on the first tree nodes; selecting second tree nodes withcorresponding average dissimilarity values equal to or greater than asecond threshold value from the tree nodes included in the regressiontree, and generating a second ruleset indicating an abnormal state ofthe target process based on the second tree nodes; and controlling thesecond process factor based on at least one of the first ruleset and thesecond ruleset.
 12. The method of claim 1, wherein the controlling thesecond process factor based on the regression tree comprises: selectinga tree node with corresponding average dissimilarity values exceeding apreset control limit from the tree nodes included in the regressiontree; generating a ruleset indicating an abnormal state of the targetprocess based on the selected tree nodes; and controlling the secondprocess factor based on the generated ruleset.
 13. The method of claim1, wherein the second process factor comprises a third process factorand a fourth process factor, wherein the regression tree comprises aplurality of layers comprising a first layer and a second layer, whereintree nodes located in the first layer are divided by the first processfactor, tree nodes located in the second layer are divided by the secondprocess factor, and the first layer is a layer higher than the secondlayer, wherein the controlling the second process factor based on theregression tree comprises: assigning respective priorities to the thirdprocess factor and the fourth process factor such that the third processfactor has higher priority than the fourth process factor; andcontrolling the second process factor by adjusting the third processfactor and the fourth process factor according to the respectivepriorities.